In the orthogonal frequency division multiplexing system, a relatively common and simple method for estimating a received signal noise variance is to use a modulus square of a difference between a channel estimation signal obtained in a pilot position and a received signal as an observed quantity, and filter or average pilot of the observed quantity located on different subcarriers and OFDM symbols to obtain estimation of the noise variance. The most advantage of this algorithm is simple operation and low complexity, but there are large errors in its result.
In order to obtain smaller estimation errors of the noise variance, different scholars have proposed different algorithms, such as an algorithm calculating channel time domain impulse response based on Inverse Fast Fourier Transform (IFFT) for pilot (mode 1), an algorithm based on autocorrelation function singular value decomposition for channel frequency domain impulse response (mode 2) and an algorithm based on QR decomposition for Fast Fourier Transform (FFT) operator (mode 3).
Taking the algorithm based on IFFT for pilot as an example, the basic operation and characteristics of such an algorithm are explained. Frequency domain channel impulse response of an OFDM frequency domain received signal is FFT/Discrete Fourier Transform (DFT) of time domain impulse response thereof. If the IFFT/IDFT is performed on one OFDM frequency domain received pilot symbol, channel time domain impulse response can be obtained. Generally, time expansion of one multipath channel is limited. Therefore, a portion of the obtained channel time domain impulse response beyond maximum time delay of the channel is pure noise. As shown in FIG. 1, in the pure noise portion, i.e., the time domain Additive White Gaussion Noise (AWGN) portion, a modulus square of each time sampling point is calculated and then averaged to obtain estimation of the OFDM received signal noise variance. Errors in the estimation result of this algorithm are much less than that of the first algorithm mentioned above, however its operation has one more N point IFFT than the first algorithm and thus is more complex. The algorithm principles of the algorithm based on autocorrelation function singular value decomposition for channel frequency domain impulse response (mode 2) and the algorithm based on QR decomposition for Fast Fourier Transform (FFT) operator (mode 3), similar to that of the algorithm based on IFFT, are both used for estimating the noise variance by calculating the variance of the pure noise portion beyond the channel time domain impulse response, and errors in their results are less than the first algorithm and thus they are more complex.
In addition, the algorithm based on IFFT as shown in FIG. 1 also has another weakness. Because it is impossible that each multipath time delay for the actual multipath channel falls on an integral multiple of sampling interval of a receiver exactly, splitting of the multiple paths in an indefinite time is inevitably resulted in. Furthermore, in the actual OFDM system, a virtual carrier set to zero physically is introduced in frequency domain due to transition protection between different frequency bands, resulting in infinite expansion of the channel time domain impulse response subsequent to the IFFT as well. The infinite expansion of the channel time domain impulse response caused by the two effects described above will cause increase in the estimation errors of the noise variance.